Cue cheesy 90s card game anime music in the background: https://www.youtube.com/watch?v=z-nkP4AdijQ

Playing something in your support slot that won't actually support your main element is totally legal. It uses up a turn, though, so it's best not to be reckless with that move.

To go over score, we simply compare each player's board states. For this example, I will be using the term "core" in place of main element for consistency's sake. In addition, I'm providing the pentagram of relations to anyone who wishes to follow along: https://puu.sh/AhbFQ/71b278dad8.jpg (top pentagram is attack relations, bottom pentagram is support relations)

Medrash has a water core, one wind support, three water attacks and one fire attack.
Salrie has a wind core, one wood support, one earth support, and three earth attacks.

As discussed in page 18, Medrash already has 1 point from his wind support. His remaining points depended on what Salrie's core was. Because it is wind, Medrash only gains 2 points from his fire attack. His water attacks are useless. Medrash's total points are 3.

Salrie gains 1 point for his earth supporting wind. His wood support does nothing. Medrash also gains 6 points; 2 points for each of his 3 earth attacks. Salrie has a total score of 7. Salrie wins.